Exponential vs Algebraic Growth and Transition Prediction in Boundary Layer Flow

Levin, Ori; Henningson, Dan S.

doi:10.1023/b:appl.0000004918.05683.46

Cited by 42 publications

(18 citation statements)

References 31 publications

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“…The streak profiles extracted from the linearized boundary layer code 31 are normalized so as to have the low-speed region at the center of the computational domain ͑z =0͒ ͑cf. Fig.…”

Section: ͑2͒mentioning

confidence: 99%

Streak interactions and breakdown in boundary layer flows

Brandt

Lange

2008

Physics of Fluids

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The objective of this paper is to show that the interaction of streamwise velocity streaks of finite length can lead to turbulent breakdown in the flat-plate boundary layer flow. The work is motivated by previous numerical and experimental studies of transitional flows where the high-frequency oscillations leading to turbulence are seen to form in the region of strongest shear induced by streaks in relative motion. Therefore, a model for the interaction of steady and unsteady ͑i.e., slowly moving in the spanwise direction͒ spanwise periodic streaks is proposed. The interaction of two subsequent streaks is investigated for varying collision parameters. In particular, the relative spanwise position and angle are considered. The results show that the interaction is able to produce both a symmetric and asymmetric breakdown without the need for additional random noise from the main stream. Velocity structures characteristic of both scenarios are analyzed. Hairpin and ⌳ vortices are found in the case of symmetric collision between a low-speed region and an incoming high-speed streak, when a region of strong wall-normal shear is induced. Alternatively, when the incoming high-momentum fluid is misaligned with the low-speed streak in front, single quasi-streamwise vortices are identified. Despite the different symmetry at the breakdown, the detrimental interaction involves for both cases the tail of a low-speed region and the head of a high-speed streak. Further, the breakdown appears in both scenarios as an instability of three-dimensional shear layers formed between the two streaks. The streak interaction scenario is suggested to be of relevance for turbulence production in wall-bounded flows.

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“…The streak profiles extracted from the linearized boundary layer code 31 are normalized so as to have the low-speed region at the center of the computational domain ͑z =0͒ ͑cf. Fig.…”

Section: ͑2͒mentioning

confidence: 99%

Streak interactions and breakdown in boundary layer flows

Brandt

Lange

2008

Physics of Fluids

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“…These are computed with a spectral code used in Ref. 8 adjoint optimization technique described in Ref. 10.…”

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confidence: 99%

The stabilizing effect of streaks on Tollmien-Schlichting and oblique waves: A parametric study

Bagheri

Hanifi

2007

Physics of Fluids

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The stabilizing effect of finite amplitude streaks on the linear growth of unstable perturbations ͓Tollmien-Schlichting ͑TS͒ and oblique waves͔ is numerically investigated by means of the nonlinear parabolized stability equations. We have found that for stabilization of a TS-wave, there exists an "optimal" spanwise spacing of the streaks. These streaks reach their maximum amplitudes close to the first neutral point of the TS-wave and induce the largest distortion of the mean flow in the unstable region of the TS-wave. For such a distribution, the required streak amplitude for complete stabilization of a given TS-wave is considerably lower than for ␤ = 0.45, which is the optimal for streak growth and used in previous studies. We have also observed a damping effect of streaks on the growth rate of oblique waves in Blasius boundary layer and for TS-waves in Falkner-Skan boundary layers.In boundary-layer flows, the transition from a laminar state to a turbulent one is usually caused by growth and breakdown of small amplitude perturbations. For a long time, the common understanding has been that any kind of flow perturbation inside the boundary layer has a promoting effect on transition. However, a number of recent studies 1-4 have indicated that certain types of perturbations inside the boundary layer can postpone the laminar-turbulent transition. A general feature of these perturbations seems to be a modification of mean velocity profile to a more stable one. In two-dimensional mean flows, these are streaky structures that create regions of alternating negative and positive streamwise velocity perturbations. Streaks are usually found inside the boundary layers subjected to high free-stream turbulence. A damping effect of moderate amplitude free-stream turbulence on Tollmien-Schlichting ͑TS͒ waves has been observed in some experiments. 5 Numerical investigations of Cossu and Brandt 2 showed a clear stabilizing effect of streaks on growth of TS waves in Blasius flow. They reported an increasing damping effect with increasing streak amplitude. These results were later verified by experimental works of Fransson et al., 3 who generated the streaks by means of small roughness elements. Recently, Fransson et al. 4 also showed that these streaks can truly delay the transition. Here, the transition was triggered by means of highamplitude two-dimensional disturbances generated through random suction and blowing at the wall. These new results have received great attention; e.g., Ref. 6. However, in all these studies, both experimental and numerical, a single spanwise spacing ͑␤ = 0.45͒ of streaks has been used, which corresponds to the most growing streaks. Therefore, we aim to investigate whether other distributions of streaks are more efficient for stabilizing TS-waves, so that a lower streak amplitude would be required for transition delay. This is important because the amplitude of the streaks should not exceed the threshold for secondary instability and instead promoting the transition to turbulence. The present work is...

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“…The advantage of the PSE-based formulation is that it is also applicable to more complex base flows, where the flow evolves slowly along the streamwise direction but the boundary-layer approximation may not hold, and that it can be easily extended to unsteady disturbances. Reference [38] provides a detailed comparison between both formulations for incompressible flows. Although infinite Reynolds number asymptotic results cannot be directly computed using the PSE, good agreement is achieved between the two methodologies for both incompressible and compressible regimes, as shown in Sec.…”

Section: Methodsmentioning

confidence: 99%

Optimal Growth in Hypersonic Boundary Layers

Paredes

Choudhari

et al. 2016

AIAA Journal

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The linear form of the parabolized linear stability equations is used in a variational approach to extend the previous body of results for the optimal, nonmodal disturbance growth in boundary-layer flows. This paper investigates the optimal growth characteristics in the hypersonic Mach number regime without any high-enthalpy effects. The influence of wall cooling is studied, with particular emphasis on the role of the initial disturbance location and the value of the spanwise wave number that leads to the maximum energy growth up to a specified location. Unlike previous predictions that used a basic state obtained from a self-similar solution to the boundary-layer equations, mean flow solutions based on the full Navier-Stokes equations are used in select cases to help account for the viscousinviscid interaction near the leading edge of the plate and for the weak shock wave emanating from that region. Using the full Navier-Stokes mean flow is shown to result in further reduction with Mach number in the magnitude of optimal growth relative to the predictions based on the self-similar approximation to the base flow. Nomenclature A, B, C, D = linear matrix operators c = normalization coefficient E = total energy norm G = energy gain h 1 = streamwise metric factor h 3 = spanwise metric factor J = objective function K = kinetic energy norm K = bilinear concomitant L = flat-plate characteristic length L = Lagrangian function M = Mach number M E = energy weight matrix N = logarithmic amplitude ratio relative to neutral stability location of modal instability N η = number of discretization points along the wall-normal direction q = vector of base flow variables q = vector of perturbation variableŝ q = vector of amplitude variables R = local Reynolds number Re = Reynolds number T = temperature T ad = adiabatic wall temperature T w = wall temperature u; v; w = streamwise, wall-normal, and spanwise velocity components ν = kinematic viscosity x; y; z = Cartesian coordinates α = streamwise wave number β = spanwise wave number γ = heat capacity ratio δ = local similarity length scale of boundary layer δ 0.995 = 0.995 boundary-layer thickness ξ; η; ζ = streamwise, wall-normal, and spanwise coordinates in body-fitted coordinate system ρ = density Ω = domain of integration ω = angular frequency Subscripts ad = adiabatic wall condition r = reference value w = wall condition 0 = initial disturbance location 1 = final optimization location Superscripts H = conjugate transpose T = transpose = dimensional value † = adjoint

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Exponential vs Algebraic Growth and Transition Prediction in Boundary Layer Flow

Cited by 42 publications

References 31 publications

Streak interactions and breakdown in boundary layer flows

Streak interactions and breakdown in boundary layer flows

The stabilizing effect of streaks on Tollmien-Schlichting and oblique waves: A parametric study

Optimal Growth in Hypersonic Boundary Layers

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